Spin(2,3) Global Path Selection v17: Two-Mode Mixing Exhaustion
Frozen: 23 October 2026
The missing stabilized axion--torsion sector has now been solved at the most general quadratic low-energy level. Positive kinetic and mass matrices give healthy poles and a conserved total source-residue norm, but leave the coupling assigned to either mass eigenstate continuously variable.
| ID | Path | State | Result or blocker |
|---|---|---|---|
| TG | Three-generation \(E_6\) quotient | completed | topology fixes three net generations |
| TM | General healthy two-mode reduction | completed | exact canonicalization and pole decomposition |
| RS | Residue norm selects \(1/8\) | rejected as selector | only \(h_1^2+h_2^2=g^TK^{-1}g\) is invariant |
| SV | Microscopic stabilized torsional vacuum | externally blocked | compactification must calculate \(K,M^2,g\) and thresholds |
| FP | Nonperturbative fixed point | externally blocked | complete quantum packet absent |
The low-energy surrogate has therefore been exhausted without assuming a microscopic vacuum. It proves that health and topology do not determine the mixing angle. Further string progress requires construction of the vacuum that supplies its matrices; further field-theory progress requires the full quantum packet.
Reproduction
node verification/verify/verify_spin23_axion_torsion_two_mode_mixing.mjs
node verification/verify/verify_spin23_new_model_path_selection_v5.mjs